The problem isn't mental toughness. If you make something a test of willpower, that something will always win, because willpower eventually runs out. At some point, physiology wins.
Yes, you should be able to hit 10:00...but what's your 5K time? It might just be a matter of your needing more aerobic endurance. Lots of people do in HS. Run more miles, do more tempo runs, do more long intervals. If you're right on the edge the whole time you're racing, you can't race smart.
Or if your endurance is OK, then look carefully at your splits, especially the first 200/400. If you go out too fast, you put yourself on the edge for the rest of the race. Force yourself to take the first 200 in 37.5 and the first lap in 75. Stay on pace.
Or it might just be race experience. Have you run the 3200 a lot? You should feel completely in control running 5:00 pace so that you can execute your race plan over the last 600m.
Mental toughness isn't something that shows up at the end of the race. You show mental toughness by training consistently and racing intelligently over the first 6 laps. If you don't do that, being tough won't help you. If you are doing that, then you don't need mental toughness. Just fitness, patience, and experience.